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Quantification of uncertainty in production forecasting is an important aspect of reservoir simulation studies. The uncertainty in the forecasting stems from the uncertainties of various model-input parameters, such as permeability, porosity, relative permeability endpoints, etc. Traditionally, the outcome of history matching is a set of parameter values that result in a good match of the historical production data. Clearly, the history matching process will be even more valuable if the uncertainties of these model-input parameters can be quantified in the process. In this paper, we present a systematic history matching approach to condition a reservoir model to production data and quantify the uncertainties of history matching parameters in terms of probability density functions. The new approach utilizes experimental design and multi-objective global optimization techniques. More specifically, for a given list of uncertain parameters, the history matching process is treated as a combinatorial optimization problem to find the best combination of these parameters to achieve the minimum history match error. The combinatorial optimization problem is solved by applying a hybrid metaheuristic method that combines evolutionary algorithms, Tabu search, and experimental design techniques. In the optimization process, reservoir models containing different combinations of parameter values are automatically generated to cover a wide range of possibilities based on the principles of experimental design and Tabu search. The search space of the optimization problem is gradually reduced by adopting the natural selection mechanism to discard parameter values that do not fit field data. Finally, the posterior probability density functions of the uncertain parameters are estimated by applying Bayesian theory. The proposed methodology is demonstrated in a real field case study of a complex oil field, which has 12 production wells and 10 years of production history. Some of the wells in the reservoir are found to be difficult to match using the traditional manual history matching approach. After applying the new approach, all the well histories are successfully matched. More importantly, the posterior probability density functions of uncertain parameters are estimated in the history matching process. The results can be further used to quantify the uncertainty in the production forecasting of follow-up recovery processes. Introduction Traditionally, history matching is done manually by varying a few reservoir parameters until a satisfactory match is obtained. It is often the most tedious and time-consuming task in a reservoir simulation study project. Limited by the time frame available, the manual trial-and-error approach usually leads only to a single matched model and provides very little information on the uncertainties of the model. History matching is by nature a very complex non-linear and ill-posed inverse problem. Like most inverse problems, it is characterized by the non-uniqueness of the solution, which means that different combinations of model parameter values may yield similar acceptable matches of the reservoir historical data. In order to achieve a better understanding of the uncertainties of the reservoir, it is necessary to obtain as many multiple good matches as possible in the history matching process1–3.

In-situ combustion (ISC) is a promising enhanced oil recovery process for the vast heavy oil accumulation of the Orinoco Belt in Venezuela. Combustion tube tests were performed to assess the feasibility of the process in a reservoir of the area. Given the successful laboratory results, it was decided to proceed with the design of a pilot test. Along with the basic design calculations, a simulation model was built to aid in selecting optimum well locations and operating strategies of the pilot. This would also be used for history matching of the actual operation and further optimization. One of the features of the model is the inclusion of the foamy oil behavior exhibited by the oil. For the modeling of the combustion process, a kinetic model developed in-house by PDVSA Intevep using thermo-gravimetric and scanning calorimetry experiments from an analog field, was employed. The first stage of the study involved the characterization of the oil into the same pseudo-components utilized by the kinetic model. A match of relevant PVT data was done for this purpose. In the second stage, the field scale model was history matched with the new fluid model, which included the foamy oil behavior. The best agreement with field measured data was obtained with a dispersed-gas foamy oil model with velocity dependence of the reaction that converts the low-mobility dispersed gas into high-mobility free gas. The following stage consisted of the history match of the combustion tube test, which was partly achieved with an assisted-history-matching tool. In the last stage, the results obtained from the combustion tube match were applied to the field model. In order to determine the most appropriate locations of production and injection wells, several pilot configurations were studied combining vertical and horizontal wells. A sensitivity analysis was completed using operational parameters such as injection rates and distance between producers and injectors wells. Based on ultimate recovery, the best pattern configuration was selected along with the optimum operational parameters. This paper illustrates the application of a workflow for modeling ISC from laboratory experiments to the field scale.

Various studies have shown that optimization of SAGD well locations and operating conditions has a great potential to improve the economics of SAGD operations. However, such optimization often ignores geological uncertainties of the reservoir and is based on a single realization. Due to the significant impact of reservoir properties on SAGD performance, the optimal solution obtained based on a single realization may deviate severely from the actual optimality. This paper presents a SAGD optimization workflow which takes into account geological uncertainties of the reservoir. To capture geological uncertainties, a large number of realizations need to be generated honoring geological constraints. Due to the high computational cost of SAGD simulations, it is impractical to use all realizations in the optimization workflow. So the first step of the workflow is to select a small set of realizations that represent the overall uncertainty of the reservoir. This is achieved by ranking all realizations according to the performance of each realization in terms of net present value (NPV) under the base operating conditions. Based on the ranking, a small set of representative realizations are chosen to represent the overall uncertainty of the reservoir. With the selected representative realizations, a robust optimization methodology is applied to account for the uncertainty of the reservoir model. In robust optimization, the decision-maker seeks an optimal risk weighted solution that is most likely to give good performance for any realization of the uncertainty in a given set. The robust optimization objective consists of two components: the expected value and standard deviation of NPV over the set of representative realizations. The weighting of the standard deviation term can be adjusted to reflect the risk tolerance of the decision-maker. Finally, the robust optimization problem is solved using an optimization algorithm assisted by second-order polynomial proxy models. The robust optimization procedure is applied to a SAGD model with three well pairs and 100 realizations. The results are compared with the optimization results obtained from a single realization (nominal optimization). The comparison shows that the robust optimization workflow not only increases the average NPV but also increases all the NPV percentile values (P10, P20, …, P90). This indicates the increased robustness of the optimal solution under geological uncertainties and thus, adoption of the robust optimization procedure can significantly reduce the project risk.

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